Matthew was given a gift card for a coffee shop. Each morning, Matthew uses the card to buy one cup of coffee. Each cup of coffee costs $4 and after buying 3 cups of coffee, the card had a $8 remaining balance. Write an equation for A, commaA, in terms of x, commax, representing the amount money remaining on the card after buying xx cups of coffee.

We are asked to write an equation for $ A $, representing the amount of money remaining on Matthew's gift card after buying $ x $ cups of coffee.

### Problem Breakdown:

- Each cup of coffee costs $4.
- After buying 3 cups of coffee, $8 remains on the card.
  
Let's represent the initial balance on the card as $ B $.

#### Step 1: Write an equation for the remaining balance.
After buying $ x $ cups of coffee, the total amount spent is $ 4x $, because each cup costs $4.

The remaining balance $ A $ on the card is then:
\[
A = B - 4x
\]

#### Step 2: Use the given information to solve for $ B $.
We know that after 3 cups of coffee, the remaining balance is $8. So, when $ x = 3 $, we can substitute into the equation:
\[
8 = B - 4(3)
\]
\[
8 = B - 12
\]
\[
B = 20
\]

Thus, the initial balance on the card was $20.

#### Step 3: Final equation.
Now that we know $ B = 20 $, we can substitute this back into the original equation:
\[
A = 20 - 4x
\]

This is the equation representing the remaining balance $ A $ after buying $ x $ cups of coffee.

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Would you like more details or have any questions? Here are 5 related questions to deepen your understanding:

1. What would the remaining balance be after 5 cups of coffee?
2. How many cups of coffee can Matthew buy before his card runs out of money?
3. If the price of each cup of coffee increased to $5, how would the equation change?
4. Can we determine the maximum amount of coffee Matthew can buy with a $50 gift card?
5. How would the equation change if the coffee shop offered a 10% discount on each cup of coffee?

**Tip:** When solving for unknown variables, always double-check units and terms to ensure they align with the problem's context.

Matthew was given a gift card for a coffee shop. Each morning, Matthew uses the card to buy one cup of coffee. Each cup of coffee costs $4 and after buying 3 cups of coffee, the card had a $8 remaining balance. Write an equation for A, in terms of x, representing the amount of money remaining on the card after buying x cups of coffee.

Learn how to write a linear equation representing the remaining balance on Matthew's gift card after buying cups of coffee. This problem involves algebraic concepts and is suitable for students in Grades 6-8. Solve for the initial balance and create a formula for the remaining amount after purchasing x cups of coffee.

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